In this paper, we prove that the dimension of the space spanned by the characters of the symmetric powers of the standard n-dimensional representation of Sn is asymptotic to n2/2. This is proved by using generating functions to obtain formulas for upper and lower bounds, both asymptotic to n2/2, for this dimension. In particular, for n ≥ 7, these characters do not span the full space of class functions on Sn.
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics